Remark 5.5.4 
Using Schur functors (see [1]}), one can express the Hodge structure of \(\widetilde{M}\)  purely in terms of \(U\) . In particular, one can show that
\(H^*(\widetilde{M}) = \operatorname{Sym}^3U \oplus \Lambda ^3U \oplus (U^{\otimes 2})^{\oplus 2}\langle 1 \rangle \oplus U^{\oplus 138}\langle 2 \rangle \oplus \mathbb {Q}^{\oplus 512}\langle 3 \rangle ,\) 
